Male or female

Probability Level pending

A family has 8 8 children, what is the probability that they have 5 5 boys and 3 3 girls? Assume that the probability of a male birth and a female birth is 1 2 \dfrac{1}{2} . Give your answer correct to five decimal places.


The answer is 0.21875.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

By the binomial coefficient, we have

P = n C r ( p r ) ( q n − r ) = 8 C 5 ( 1 2 ) 5 ( 1 2 ) 3 = P=nCr(p^r)(q^{n-r})=8C5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^3= 0.21875 \color{#D61F06}\boxed{0.21875}

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